Table of Contents

Lipsey & Wilson (2001)

The Methods and Data

The book Practical meta-analysis by Lipsey and Wilson (2001) is an excellent introduction to meta-analysis and covers in less than 250 pages the most important aspects of conducting a meta-analysis. Here, I will reproduce the analyses conducted in chapter 7, which is focused on the computational aspects of a meta-analysis, including the fixed-, random-, and the mixed-effects model. The data are provided in the book on page 130 in Table 7.1. We can create the same dataset with:

Weighted Regression Analysis

The "weighted regression analysis" described on pages 138-140 is again nothing else than a fixed-effects model with moderators. Here, the authors are including both the random and the intensity moderators in the model. This can be done with:

Heterogeneity Accounted For

The amount of heterogeneity accounted for by the moderator(s) included in the model is typically computed by comparing the amount of heterogeneity from the random-effects model with the amount of residual heterogeneity from the mixed-effects model (for more details, see the FAQs). The value is given in the output above. We can also carry out this computation explicitly with:

The value under R^2 is the amount of variance (heterogeneity) accounted for. In this particular example, we estimate that 81.2% of the total amount of heterogeneity is accounted for by the two moderators. Note that Lipsey and Wilson calculate $R^2$ in a different way than is usually done in meta-analyses, so the value for $R^2$ shown in Exhibit 7.7 (page 141) is different from the value computed above.